7/6-4/3n=-3/2n+2

Solution for 7/6-4/3n=-3/2n+2 equation:

7/6-4/3n=-3/2n+2

We move all terms to the left:

7/6-4/3n-(-3/2n+2)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 2n+2)!=0

n∈R


We get rid of parentheses

-4/3n+3/2n-2+7/6=0

We calculate fractions


84n^2/216n^2+(-288n)/216n^2+324n/216n^2-2=0

We multiply all the terms by the denominator


84n^2+(-288n)+324n-2*216n^2=0

We add all the numbers together, and all the variables

84n^2+324n+(-288n)-2*216n^2=0

Wy multiply elements

84n^2-432n^2+324n+(-288n)=0

We get rid of parentheses

84n^2-432n^2+324n-288n=0

We add all the numbers together, and all the variables

-348n^2+36n=0

a = -348; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-348)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-348}=\frac{-72}{-696}
=3/29
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-348}=\frac{0}{-696}
=0
$